Geodesic
Moscow talk: the theorem on approximation of trigonometric sum by a short one (ATS)
Čebyševskij sbornik, Tome 16 (2015) no. 1, pp. 6-18.

Voir la notice de l'article provenant de la source Math-Net.Ru

The invited talk presented at the seminar of Prof. B. S. Kashin and Prof. S. V. Konyagin at the Faculty of Mechanics and Mathematics of Moscow Lomonosow University at the November 9, 2006. Bibliography: 15 titles.
Keywords: trigonometric sum, approximation, Voronoi’ formula, the Poisson summation formula, the theorem ATS. 
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A. A. Karatsuba. Moscow talk: the theorem on approximation of trigonometric sum by a short one (ATS). Čebyševskij sbornik, Tome 16 (2015) no. 1, pp. 6-18. http://geodesic.mathdoc.fr/item/CHEB_2015_16_1_a0/

[1] Karatsuba A. A., “Approximation of exponential sums by shorter ones”, Proc. Indian. Acad. Sci. (Math. Sci.), 97:1–3 (1987), 167–178 | DOI

[2] Voronin S. M., Karatsuba A. A., The Riemann zeta-function, Phys.-Math. Lit., M., 1994, 376 pp. (Russian)

[3] Voronoi G., “Sur un probléme du calcul des fonctions asymptotiques”, Journal für die reine und angewandte Mathematik, 126 (1903), 241–282

[4] Hardy G. H., Littlewood J. E., “The trigonometrical series associated with the elliptic $\theta$-functions”, Acta Math., 37 (1914), 193–239 | DOI

[5] Vinogradov I. M., “On the average value of the number of classes of purely root form of the negative determinant”, Communications of Kharkhov Mathematics Society, 16 (1917), 10–38

[6] Van der Corput J. G., “Verschärfung der abschätzung beim teilerproblem”, Math. Ann., 87 (1922), 39–65 | DOI

[7] Vinogradov I. M., Special Variants of the Method of Trigonometric Sums, Nauka, M., 1976, 122 pp.

[8] Karatsuba A. A., “On the distance between adjacent zeros of the Riemann zeta function lying on the critical line”, Proc. Steklov Inst. Math., 157, 1983, 51–66

[9] Mozer Ya., “Ob odnoi summe v teorii dzeta-funktsii Rimana”, Asta Arith., 31 (1976), 31–43; Acta Arith., 31 (1976), 31–43; 31 (1976), 45–51; 35 (1979), 403–404; 40 (1981), 97–107 [Moser J., “On a certain sum in the theory of the Riemann zeta-function”]; Correction to the paper: Acta Arith., 31 (1976), 31–43; 31 (1976), 45–51; 35 (1979), 403–404; 40 (1981), 97–107

[10] Ivic A., Topics in Recent Zeta-Function Theory, Publ. Math. d'Orsay, Universite de Paris-Sud, Orsay, 1983, 272 pp.

[11] Narozhny N. B., Sanchez-Mondragon J. J., Eberly J. H., “Coherence versus incoherence: collapse and revival in a single quantum model”, Phys. Rev. A, 23 (1981), 236–247 | DOI

[12] Fleischhauer M., Schleich W. P., “Revivals made simple: Poisson summation formula as a key to the revivals in the Jaynes–Cummings model”, Phys. Rev. A, 47:3 (1993), 4258–4269 | DOI

[13] Chassande-Mottin E., Pai A., “Best chirplet chain: Near-optimal detection of gravitational wave chirps”, Physical Review D, 73 (2006), 042003, 23 pp. | DOI

[14] Karatsuba E. A., “Approximation of sums of oscillating summands in certain physical problems”, Journal of Math. Physics, 45:11 (2004), 4310–4321 | DOI

[15] Karatsuba E. A., “Approximation of exponential sums in the problem on the oscillator motion caused by pushes”, Chebyshevskii Sb., 6:3(15) (2005), 205–224